An aircraft has an initial mass of m0 and an initial acceleration of a0. After flying for 2 hours, the mass of the aircraft has decreased by 11%, due to the burning of the fuel. If the propulsive force provided by the engines is constant, what is the expression for the new acceleration, a2, at this time? You may assume that the aircraft is in level flight at all times and the air resistance is negligible.
Select one:
a. a2=0.89a0
b. a2=a0/0.89
c. a2=1.11a0
d. a2=1+0.11a0
b. a2=a0/0.89
To determine the expression for the new acceleration, a2, we need to consider the concept of inertia and the relationship between force, mass, and acceleration.
According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Initially, the mass of the aircraft is m0, and the acceleration is a0. Therefore, the initial force acting on the aircraft is:
F0 = m0 * a0
After flying for 2 hours, the mass decreases by 11%. This means that the new mass, m2, is given by:
m2 = m0 - 0.11 * m0
= m0 * (1 - 0.11)
= m0 * 0.89
Now, let's find the expression for the new acceleration, a2. The force acting on the aircraft remains constant, as the propulsive force provided by the engines is constant. Therefore, we can equate the initial force (F0) to the new force (F2):
F0 = F2
Since force is equal to mass multiplied by acceleration, we have:
m0 * a0 = m2 * a2
m0 * a0 = m0 * 0.89 * a2
Simplifying the equation, we find:
a2 = a0 * 0.89
Therefore, the expression for the new acceleration, a2, is:
a2 = 0.89 * a0
Hence, the correct answer is:
a2 = 0.89a0 (Option a)
To find the expression for the new acceleration, a2, we need to consider the change in mass of the aircraft and the constant propulsive force provided by the engines.
Given that the mass of the aircraft decreases by 11% after flying for 2 hours due to the burning of fuel, we can calculate the new mass, m2, at that time.
The decrease in mass can be expressed as 11% of the initial mass, m0, which is given by:
Δm = 0.11m0
The new mass, m2, can be calculated by subtracting the decrease in mass from the initial mass:
m2 = m0 - Δm = m0 - 0.11m0 = 0.89m0
Now, let's consider Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
F = ma
We can rearrange this equation to solve for acceleration:
a = F / m
Since the propulsive force provided by the engines is constant throughout flight, the equation for acceleration becomes:
a0 = F / m0
To find the expression for the new acceleration, a2, we substitute the new mass, m2, into the equation:
a2 = F / m2
Since the force provided by the engines is constant, we can conclude that the expression for the new acceleration, a2, is:
a2 = a0 / (0.89m0)
Therefore, the correct answer is option b. a2 = a0 / 0.89.
Using Newton's second law: F=ma
and since F=constant,
we have
m0a0=m2a2
Knowing that m2/m0=(1-0.11)=0.89
you can solve for a2.
Note: it does not seem realistic that an aircraft accelerates horizontally for two hours and continue accelerating!